Prepare the ice cream maker according to its instructions. Peel and pit ripe mangoes, removing any tough fibers near the stones before weighing the flesh.
Combine water and sugar in a small saucepan. Heat gently while stirring until the sugar dissolves, then cool the syrup completely.
Blend mango, cooled syrup, lime juice, zest, and salt until very smooth. Scrape the blender sides and blend again if visible fruit pieces remain.
For fibrous mangoes, press the puree through a sieve. Cover the base and refrigerate at least 4 hours until thoroughly cold.
Churn in the prepared ice cream maker according to its instructions, usually 20–30 minutes, until the sorbet becomes thick and softly frozen.
Transfer immediately to a chilled freezer-safe container. Smooth the top, press food-safe wrapping onto the surface, and cover tightly.
Freeze at least 4 hours for a firmer scoop. Keep the container level and avoid repeatedly opening it while the mixture is setting.
Let stand 5–10 minutes before scooping if very hard. Serve in small chilled bowls and return unused sorbet to the freezer promptly.
